Question

graph the function below to find the y-intercept and state the domain, range, and the equation of the asymptote.\\( y = -4(10)^x \\)\
select all that apply.\
\\(\square\\) a) the y-intercept is \\(-4\\).\
\\(\square\\) b) the y-intercept is 10.\
\\(\square\\) c) domain: all real numbers; range: \\( y > 0 \\)\
\\(\square\\) d) domain: all real numbers; range: \\( y < 0 \\)\
\\(\square\\) e) the asymptote is \\( y = -4 \\).\
\\(\square\\) f) the asymptote is \\( y = 0 \\).

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $y=-4(10)^x$:
$y=-4(10)^0 = -4(1) = -4$

Step2: Determine domain

Exponential functions accept all real $x$, so domain is all real numbers.

Step3: Determine range

$10^x > 0$ for all real $x$, so $-4(10)^x < 0$. Range: $y < 0$.

Step4: Find horizontal asymptote

As $x\to-\infty$, $10^x\to0$, so $y\to0$. Asymptote: $y=0$.

Answer:

A) The y-intercept is -4.
D) Domain: all real numbers; Range: $y < 0$
F) The asymptote is $y = 0$.